What is the solution for y^{''}+2y^'+5y=34cos(2x) ?

The solution for y^{''}+2y^'+5y=34cos(2x) is y=e^{-x}(c_{1}cos(2x)+c_{2}sin(2x))+8sin(2x)+2cos(2x)

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y^{''}+2y^'+5y=34cos(2x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 34 cos (2 x)

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 8 sin (2 x) + 2 cos (2 x)

Solution steps

y^{''} (x) + 2 y^{'} (x) + 5 y = 34 cos (2 x)

Solve linear ODE:

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 8 sin (2 x) + 2 cos (2 x)

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 8 sin (2 x) + 2 cos (2 x)

(D^{2} - 7 D + 6) y = e^{6 x} + e^{x}

\frac{d ^{2} y}{d x ^{2}} - y = 4 e^{x} cos (x)

y^{^{''}} - y^{^{'}} - 2 x = 4 x^{2}

y^{^{''}} + 2 y^{^{'}} + 4 y = 2 t - 3 cos (2 t)

3 y^{^{''}} - 9 y^{^{'}} = sin (2 x)

What is the solution for y^{''}+2y^'+5y=34cos(2x) ?
The solution for y^{''}+2y^'+5y=34cos(2x) is y=e^{-x}(c_{1}cos(2x)+c_{2}sin(2x))+8sin(2x)+2cos(2x)